A Network-Ready Random-Access Qubits Memory ✉ Stefan Langenfeld 1 , Olivier Morin1, Matthias Körber1 and Gerhard Rempe1

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ARTICLE OPEN A network-ready random-access qubits memory ✉ Stefan Langenfeld 1 , Olivier Morin1, Matthias Körber1 and Gerhard Rempe1

Photonic qubits memories are essential ingredients of numerous quantum networking protocols. The ideal situation features quantum computing nodes that are efficiently connected to quantum communication channels via quantum interfaces. The nodes contain a set of long-lived matter qubits, the channels support the propagation of light qubits, and the interface couples light and matter qubits. Toward this vision, we here demonstrate a random-access multi-qubit write-read memory for photons using two rubidium atoms coupled to the same mode of an optical cavity, a setup that is known to feature quantum computing capabilities. We test the memory with more than ten independent photonic qubits, observe no noticeable cross-talk, and find no need for re-initialization even after ten write-read attempts. The combined write-read efficiency is 26% and the coherence time approaches 1ms. With these features, the node constitutes a promising building block for a quantum repeater and ultimately a quantum internet. npj Quantum Information (2020) 6:86 ; https://doi.org/10.1038/s41534-020-00316-8

INTRODUCTION Against this backdrop, it is still an open challenge to find a route Quantum networks enable faithful communication by exchanging toward multi-qubit memories that feature random qubit access, 1234567890():,; photonic qubits that cannot be cloned1. Networks conceived to both for writing and reading, and controlled qubit processability. generate an encryption key that is shared by two essentially Individual real atoms are ideal to achieve this goal. They have classical parties, Alice and Bob, have already been demonstrated already demonstrated, in complementary settings, their potential numerous times2,3. Future genuine quantum-mechanical and as faithful photonic qubit memories as well as qubit processors. multi-functional networks, however, will likely rely on multi- The memory facet has been achieved by strongly coupling the purpose nodes that can receive, store, send, and also process atom to an optical cavity, which enables the efficient interconver- 19 qubits4,5. To accomplish these tasks, such nodes require at least sion between stationary (matter) and flying (photonic) qubits . two processable qubits6–9. Due to the high level of isolation from the environment and For example, an elementary quantum repeater for long-distance control of all degrees of freedom, these memories can feature entanglement distribution requires a chain of nodes, each with long coherence times suitable for qubit storage20. The processor two memory qubits that are pairwise entangled with memory facet has been demonstrated numerous times with qubits in – qubits in the neighboring nodes. This entanglement is typically atomic registers21 25 but without a connection to photonic qubits, – established via photonic channels, which necessitate a corre- or with a connection to photonic qubits26 28, but in this case sponding qubit interface. In addition, such repeater nodes require without multiplexed write-read capabilities. single- and two-qubit gates to also realize efficient entanglement Here we integrate the two facets by realizing an intracavity swaps and complete Bell-state measurements. These properties, in register with two individually addressable atomic memories that essence, represent the celebrated five quantum computation plus can independently write, store, and retrieve photonic qubits. We two quantum communication criteria that were put forward by demonstrate the atom-selective absorption and emission of these DiVincenzo10. It needs to be emphasized that the criteria call for qubits by implementing several different random-access quan- two contradictory physical capabilities11: memories need isolated tum-memory protocols with up to eleven photonic qubits that are qubits, while processors necessitate coupled qubits. subsequently stored in the node without the need for re- In order to realize these nodes, the qubits can either be initialization. In addition to these new capabilities, the capacity distributed over an ensemble of (real or artificial) atoms or be of one qubit per single atom also sets a new benchmark on localized in single (real or artificial) atoms. Important achieve- scalability for constant resources29. ments for ensemble-based nodes include static-access (temporal) multiplexing where qubits are received and retrieved in a fixed order (e.g., first-in-first-out)12–15. This limitation can be resolved with spatial (dynamic-access) multiplexing instead of temporal RESULTS multiplexing. In fact, a random-access quantum memory (RAQM) Apparatus with an architecture resembling that of a classical random-access Figure 1a shows a sketch of the experimental setup. The system memory has been developed recently16,17. This device can in consists of two 87Rb atoms trapped close to the center of a high- principle receive and send an almost arbitrarily large number of finesse optical cavity with parameters (g, κ, γ)/2π = (4.9, 2.7, 3.0) qubits, limited only by the ratio of qubit coherence time to qubit MHz. Here, g denotes the single-qubit light-matter coupling access time. In the reported realization, this number was about constant at the center of the optical cavity for the 0 three. However, no scalable information processing capability on jiF ¼ 1; mF ¼ 0 $ jiF ¼ 1; mF ¼ ±1 atomic transition at a wave- and between the atomic qubits in all these ensemble nodes has length of 780 nm, and κ and γ are the cavity field and atomic been realized so far18. dipole decay rates, respectively20.

✉ 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, Garching 85748, Germany. email: [email protected]

Published in partnership with The University of New South Wales S. Langenfeld et al. 2

Fig. 1 Illustrative view of the experimental setup and key elements toward the high-fidelity memory. a Two atoms are trapped close to the waist of the cavity mode, symmetrically around the cavity axis. Via a high-NA objective, the atoms are imaged on an EMCCD camera. The same objective is used for addressing the individual atoms with a control laser beam by means of an acousto-optical deflector (AOD). b Possible cross-talk between the atoms due to their coupling to the same cavity mode. The state of an incoming photon should be mapped onto the addressed atom (A) via a stimulated Raman adiabatic passage (STIRAP) consisting of the cavity field g and the classical control field Ω. However, the unaddressed atom (B) offers a side-channel via off-resonant scattering of the photon. This leads to the storage of a random quantum state and thus a reduced fidelity. The lower part of the figure shows experimental data and a theory curve for how this effect can be 1234567890():,; minimized by increasing the single-photon detuning Δ. The error bars correspond to one standard deviation of the statistical uncertainties. c Cross-illumination of the addressing control field. The control intensity as a function of the addressing axis is shown, including a Gaussian fit yielding a full width at half maximum (FWHM) of the addressing beam of 2 μm. As a reference, white and gray regions indicate the trapping potential pattern, in which the typical spatial extent of the atomic wavefunction is about 50 nm. For small cross-illumination, only atomic configurations are used where the inter-atomic distance is at least three times the FWHM. The beam is elliptical (ratio 1:3) so that the atom positioning is less stringent in the direction of the long axis, illustrated by the ellipse in the second plot. The spacing of the atom leads to a reduced atom-cavity coupling g and thus to a reduced STIRAP efficiency (lower part). The blue-shaded rectangles highlight the trapping regions used for this work.

The two atoms are trapped in a two-dimensional optical lattice Analysis and cross-talk elimination consisting of a red-detuned standing wave applied perpendicular The main challenge for the realization of a high-fidelity multi-qubit to the cavity axis and a blue-detuned standing wave along the quantum memory lies in avoiding cross-talk between the individual cavity axis. The two atoms are spaced symmetrically around the qubit memories. This means, first, that only the illuminated atom cavity center and therefore couple equally strong to the cavity must couple to the incoming or the outgoing photonic qubit and, mode. The two cavity mirrors have asymmetric transmission second, that cross-illumination of the atoms from the STIRAP coefficients so that photons predominately leave the cavity via the control laser must be eliminated. The first issue arises from the fact high-transmission mirror. Outside the vacuum chamber, a high- that both atoms are identically coupled to the same cavity field. numerical-aperture objective is used for imaging and laser- Ideally, an incoming photon gets stored only in the addressed atom addressing of either atom30. via the described STIRAP process (Fig. 1b). However, as all initialized Both atoms are initialized by optical pumping to the atoms couple to the cavity, the incoming photon can interact with jiF ¼ 1; mF ¼ 0 ground state. Using a stimulated Raman adiabatic any atom including the unaddressed one. Scattering from this atom passage (STIRAP) technique31, a single incoming photonic qubit is can transfer the atom into a random state and in this way scramble absorbed via the application of a classical control pulse. The the fragile information encoded in the photon (Supplementary fi information encoded in the photon polarization (in the basis of Notes 2). A way out of this dilemma is that the STIRAP ef ciency can σ+ σ− be made constant over a large range of negative single-photon right and left circular polarization, and , respectively) is 31 ji¼ ; ¼ detunings Δ, and that the incoherent scattering rate scales like coherently mapped to the two atomic states F 2 mF 1 and Δ−2 fi jiF ¼ 2; m ¼À1 , respectively. Thus, circular polarizations are . Quantitatively, we optimize the memory delity by increasing F the detuning to Δ/2π = −100MHz with respect to jiF0 ¼ 1 (Fig. 1b). mapped to atomic energy eigenstates whereas elliptical and At this point, the maximum incoherent scattering probability per especially linear polarizations are mapped to superpositions of fi input photon is only (0.15 ± 0.01)%, in contrast to a coherent atomic states. In order to reduce the impact of magnetic- eld fi fl fi storage ef ciency of (38 ± 3)%. uctuations, a small magnetic guiding eld of about 44 mG is For the second issue, cross-illumination is minimized by applied along the cavity axis. Consequently, the phase of the applying the STIRAP control field via an optical addressing system: atomic superposition oscillates at twice the Larmor frequency, 30 After identifying the positions of the individual atoms via an kHz, during qubit storage, i.e., after write-in and before read-out. electron-multiplying charge-coupled device (EMCCD) camera, the This oscillation is deterministic and could be compensated by a center of mass of the two atoms is shifted to the center of the suitable setting of an optical wave plate. Finally, the stored cavity along one dimension (Fig. 1c). Note that the positions of the photonic qubit is retrieved by vacuum STIRAP, the time-reversed atoms are initially unknown. Then, a frequency-switchable radio process that is used for qubit storage. See Supplementary Notes 1 frequency (RF) source is adaptively programmed so that each for more details on the timing of the experimental sequence. individual frequency drives the same acousto-optical deflector

npj Quantum Information (2020) 86 Published in partnership with The University of New South Wales S. Langenfeld et al. 3

Table 1. Fidelities in percent of qubit memory implementations for four different input polarization combinations and two random-access possibilities.

The errors correspond to one standard deviation of the statistical uncertainties.

(AOD) in order to steer the beam onto one atom or the other (Fig. shows a reduced fidelity for linear polarization inputs, indepen- 1c). The pulse sequence on the atoms can be chosen randomly, dent of the polarization of atom B. We attribute this effect to with the only limitation being a delay time of 40 μs for switching magnetic-noise-induced decoherence, which becomes relevant at between the atoms. This access time is mainly due to the sound- this timescale as shown further below. propagation time through the AOD, which could be reduced with, Regardless of the memory sequence, the observed fidelities are e.g., an electro-optical deflection system to about 2 μs. Altogether, similar and largely independent of whether the input qubits are this allows atom-number independent and thus scalable random identical or orthogonal. This indicates a vanishing cross-talk and access to the atoms. Practically, in order to reduce cross- therefore demonstrates the high degree of isolation of the two illumination, we only use atom configurations where the atoms. We remark that in a possible application where the whole interatomic distance is at least three times the full width at half sequence is retried until both memories successfully emitted a maximum (FWHM) of the addressing beam along this direction, photon, the fidelity, as defined in Table 1, increases on average by i.e., dat−at ≥ 6 μm. For further details on the specific optical and 0.6% (not shown). electrical setup and on how the FWHM was measured at the One of the most important properties of a quantum memory is ’ atom s position, see Supplementary Notes 3. the storage time that we test using the AWBWARBR sequence. To A side effect of this separation is a small reduction of g at the this end, we vary the storage time between writing (AWBW) and positions of the atoms. This results in a slightly reduced average reading (ARBR) of both atoms. The results for atom A and atom B memory efficiency of (26 ± 3)% for the combined storage and are depicted in Fig. 2. Both atoms exhibit a coherence time of retrieval process (Fig. 1c). Nevertheless, the atom-to-photon state- more than 800 μs for linear polarizations and no measurable transfer probability that is relevant, e.g., for atom-photon decay of the fidelity for circular polarization. As in the single-atom entanglement still exceeds 60% in our system. This is to the best case, the coherence time is limited by magnetic-field fluctuations of our knowledge larger than in any other multi-qubit memory on the few mG levels. In addition, the coherence time is reduced that has been demonstrated so far. by spatially sampling the locally varying magnetic field. Indeed, the margin on the atom positions is chosen in a way to have a Random-access memory with up to 11 qubits reasonable data rate (see Supplementary Notes 4 for further We probe the memory coherence and efficiency by storing weak details). It is worth noting, that we expect no degradation of the coherent pulses (mean photon number n ¼ 1) of different coherence time for an even larger number of atoms as both atoms polarizations and performing a polarization tomography on the sample already a reasonably large region of the cavity mode. retrieved single photon. In order to test for cross-talk between the An extended case of the scenario AWBWBRAR is presented in atoms, we probe atom A and atom B with identical and Fig. 3. Here, atom B is used multiple times during the storage of orthogonal polarizations. Table 1 summarizes the measured atom A. This tests the cross-talk for systems where many qubits fidelities of the two polarization configurations for both atoms are stored and retrieved serially on a single atom as shown here in two different access patterns. Here, AW,BW and AR,BR stand for and also for future implementations where the number of atoms is writing and reading, respectively, of one of the atoms, A or B. In scaled up even further. In addition, it demonstrates that each both access patterns shown in the table, the storage of a photon atom can be used multiple times without re-initialization, allowing in atom B occurs when the qubit already stored in atom A has for higher repetition rates and potentially eliminating the need for rephased to its initial state. This timing is chosen to test for a atom-selective initialization. In orange and blue, Fig. 3b shows the maximum cross-talk that would manifest when the two input achieved fidelity and efficiency, respectively, for the reused atom B polarization change from identical to orthogonal. as a function of the number of trials. Efficiency and fidelity decay For the sequence AWBWARBR, the minimum storage time for by 0.29 and 0.44 pp per trial as predicted by theory (see both qubits is 100 μs, given by the Larmor frequency and the Supplementary Notes 5). Figure 3b also shows the efficiency and delay time of the addressing system. The storage time for the data fidelity of atom A after the ten memory trials on atom B. Although presented in Table 1 is 133 μs. For both atoms we achieve high only about 20% of the trials resulted in a successful memory fidelities for eigen- and superposition states as input, with no event, in every trial the cavity is populated and the classical notable difference compared to the single-atom case20. control field is applied, potentially leading to cross-talk as fi In the AWBWBRAR case, the read order of atoms A and B is discussed above. Nevertheless, as the achieved delity is in good swapped while all pulse timings are preserved. This results in agreement with the expectation from the coherence-time storage times of 83 and 183 μs for atom B and A, respectively. For measurement (the green guide to the eye), any cross-talk can atom B, this leads to a similar performance. In contrast, atom A be neglected even after ten trials.

Published in partnership with The University of New South Wales npj Quantum Information (2020) 86 S. Langenfeld et al. 4 DISCUSSION We have demonstrated an efficient network-ready random-access multi-qubit memory using two individually addressable single atoms. We have identified and solved multiple challenges such as qubit cross-talk, which arise when making the most important step from one to several atoms in the same high-finesse optical cavity. Given a lower bound on the store-and-retrieve efficiency of 20% and a cavity mode waist of 30 μm, up to 5 atoms can be accommodated. We estimate that this number can be easily increased to more than 20 atoms while still using the same trapping geometry, e.g. by using a tighter focus of the addressing beam while still using the same objective. As all of those atoms would still be coupled to the same cavity mode, cavity-mediated multi-qubit gates28,32 enable computation on all of them. For future implementations, deterministic and thus zero-tolerance atom positioning, as can be achieved in optical tweezer arrays33,34, would further increase capacity, data rate, and fidelity. Also, it would allow for Zeeman selective coherent driving addressed onto single atoms, resulting in more than 100 ms coherence time20. In combination with atom-photon entanglement and atom-atom gates19,28, the extension to multiple individually addressable atoms renders the cavity platform a promising candidate for future quantum networks with quantum repeaters7 and distributed quantum computers9.

DATA AVAILABILITY Fig. 2 Coherence time for both atoms. Time evolution of the The data sets generated during and/or analyzed during the current study are fidelity for the storage of circular (orange) and linear (blue) available in the zenodo repository, https://doi.org/10.5281/zenodo.4018024. polarizations for atom A and atom B. The sinusoidal fits to the 20 μs slices are fit with a Gaussian decay (green) giving a coherence Received: 26 June 2020; Accepted: 18 September 2020; time of more than 800 μs for both atoms. The error bars represent the 95% confidence intervals of the statistical uncertainties.

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